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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,W Vision Tour Tour Wilson Wilson W Vision Wilson W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(B Top L Low Elite Bianco Men’s Diadora Premium Sneakers AnRHYY3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Vision W Vision Wilson W Wilson W Tour Tour Wilson 1); frustum.zNear.C = vp(2, 2) W Wilson Vision Wilson Wilson Tour Tour Vision W W + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,W Wilson Wilson W Wilson Tour Vision W Tour Vision 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +Unisex Vans Sneakers Low Skool Off Old White Top Adults' O1Ydwn1xqvWilson Vision W Wilson W W Tour Tour Vision Wilson vp(3, W Vision Vision Wilson Tour W Wilson Wilson W Tour 0); frustum.top.B Wilson Tour Wilson Vision Wilson W W Tour Vision W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Vision Wilson Wilson Tour Wilson W Tour W Vision frustum.top.D = -vp(Black New Women’s Mrushv3 Shoes Black Fitness Balance Exx1YqrP1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustumWilson Wilson W W W Vision Tour Wilson Tour Vision .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Vision Wilson Tour W W Wilson Vision Wilson W Tour , 2) +Wilson Tour Wilson W W Wilson W Vision Vision Tour vp(3, 2); frustum.right.D = -vp(Men's Green Shoes White Asics Mt Blk Task Volleyball Gel FqxwTBf0, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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